Abstract

Progressive cracking in structural elements of concrete is considered. Two simple models are applied, which, even though different, lead to similar predictions for the fracture behaviour. Both Virtual Crack Propagation Model and Cohesive Limit Analysis (Section 2), show a trend towards brittle behaviour and catastrophical events for large structural sizes. Such a trend is fully confirmed by more refined finite element models, as well as by experimental testing on plain and reinforced concrete members.

A numerical Cohesive Crack Model is proposed (Section 3) to describe strain softening and strain localization in concrete. Such a model is able to predict the size effects of fracture mechanics accurately. A general explanation to the well-known decrease in tensile strength and increase in fracture toughness by increasing the member sizes, is given in terms of Dimensional Analysis. The true values of such two intrinsecal material properties may be found exactly only with comparatively low values of the brittleness numbers

.

Whereas for Mode I, only untieing of the finite element nodes is applied to simulate crack growth, for Mixed Mode a topological variation is required at each step (Section 4). In the case of the four point shear specimen, the load vs. deflection diagrams reveal snap-back instability for large sizes. By increasing the specimen sizes, such instability tends to reproduce the classical LEFM instability. Experimentally, the fracture toughness of concrete appears to be unique and represented by the Mode I fracture energy even for Mixed Mode problems.

Remarkable size effects are theoretically predicted and experimentally confirmed also for reinforced concrete (Section 5). The brittleness of the flexural members increases by increasing size and/or decreasing steel content. On the other hand, a physically similar behaviour is revealed in the cases where the brittleness number

is the same. On the basis of these results, the empirical code rules regarding the minimum amount of reinforcement could be considerably revised.